C₃×C₂²⋊#1039 #11925206

order	1200
isoclinism	isoclinic class of #6045
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂²×C₅

Aliases

Hall	C₃×C₅² ⋊ C₂²⋊C₄
Sylow	C₅² ⋊ C₃×C₂²⋊C₄

272 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 600

A minimal faithful permutation representation — 3 generators on 21 points:

(1,2,3)(9,11)(17,18,20,21,19);(4,5,6,7)(8,9)(10,11)(13,14)(15,16)(18,19)(20,21);(12,13,15,16,14)

318 conjugacy classes. The character table is too large to display.

maximal subgroup of	C₃×C₂²⋊C₄×C₅⋊D₅, C₃×#11717257, C₃×#11717273, …
maximal normal subgroup of	C₃×C₂²⋊C₄×C₅⋊D₅, C₃×#11717257, C₃×#11717273, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 416);